ISOPERIMETRIC INEQUALITY AND CURVES OF CONSTANT WIDTH
Among all two-dimensional geometrical objects, a circle is one of some important <br /> <br /> <br /> things considered by geometers. There is an interesting theorem related to it, <br /> <br /> <br /> which we called isoperimetric inequality. This theorem say...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/24387 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Among all two-dimensional geometrical objects, a circle is one of some important <br />
<br />
<br />
things considered by geometers. There is an interesting theorem related to it, <br />
<br />
<br />
which we called isoperimetric inequality. This theorem says that the area of the <br />
<br />
<br />
domain enclosed by a simple closed curve will be maximum if the curve is a <br />
<br />
<br />
circle. meanwhile, a curve of constant width is good for study, since it has a unique <br />
<br />
<br />
property that is the same as circle’s. Reuleaux triangle is a famous example of such <br />
<br />
<br />
class of curves. <br />
<br />
<br />
The aim of this thesis is to prove isoperimetric inequality using Fourier series, <br />
<br />
<br />
studying properties of curves of constant width using a special function called <br />
<br />
<br />
support function, and comparing Reuleaux triangle and its variance with a curve <br />
<br />
<br />
related to them by using support function. |
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